Feeling sort of isolated, but don’t want to be a smothering girlfriend

So there was a gathering with a bunch of people a few days ago with food, games, just things outside. I went with my boyfriend and we walk in and both get drinks, but as soon as we're done getting drinks he sees his friend group playing frisbee, and asks if I want to play frisbee with them. That sounds fun to me so we both walk over and as soon as he sees them he leaves me standing there to go play with them, completely forgetting about me. Keep in mind that I'm not friends with his friends and, maybe this is my fault, but I didn't try to go introduce myself to them. Seeing my boyfriend just walk off without trying to include me and seemingly forgetting I was there didn't make me want to really be there anymore. For the rest of the night, I just sat around with one of my girlfriends. Later in the evening, I decided I needed to put myself into their group in order to be involved, so I walk over to where they're playing frisbee and I notice that my boyfriend is having so much fun. I know this is going to sound smothering and selfish but he never seems to have as much fun with me as he does with his friends. It isn't like he never sees these people either, he sees them all every day. And every time I'm with him and he hangs out with them this sort of thing happens and I feel like he's forgetting about me. When I was eating, he sat close enough to me to definitely see me, but instead turns and sits with his friends. I would be happy for him to bring his friends over and we all sit together and eat, he didn't even say anything to me. When I was playing frisbee with him and his friends he was first saying things like ”what have you been doing?” ”are you having fun” but after that, it was like I was ignored again. He played frisbee with me once or twice and then just never passed it to me again after that. So I just stood there awkwardly while they played and has a blast. My girlfriend was long gone by then anyway. When his friends left, that's the only time he actually paid attention to me and played frisbee and threw a football and stuff with me. It seemed like he thought that was a chore or something he had to do. He wasn't having any fun. Another example of something bothering me is when I told him about my period and cramps and stuff and I was telling him that I was actually bothered by them, and he just says ”eww” kind of in a joking voice and quits the conversation. I know he isn't actually grossed out by periods, it just seems like he simply doesn't care. I don't want to be a bad girlfriend, I really do love him. I want to let him have fun and do things without me, but it seems like he feels like he has to do things with me because I'm his girlfriend, he doesn't actually want to.